Bayesian Two-Way Analysis of High-Dimensional Collinear Metabolomics Data

Kaksisuuntainen tehtävänasettelu on yleinen bioinformatiikan alalla. Tässä diplomityössä esitellään uusi bayesilaisen mallinnuksen menetelmä kaksisuuntaisen havaintoaineiston analysointiin. Menetelmä toimii myös vähän näytteitä sisältävillä korkeaulotteisilla havaintoaineistoilla. Havaintoaineiston oletetaan jakautuvan populaatioihin kovariaattien mukaan, jotka tyypillisessä biologisessa kokeessa ovat yksilön terveydentila, sukupuoli, lääketieteellinen hoito sekä yksilön ikä. Esiteltävä menetelmä on suunniteltu arvioimaan näiden kovariaattien vaikutus havaintoaineiston kontrolliryhmän perustasoon verrattuna. Menetelmä perustuu olettamukseen siitä, että havaintoaineiston piirteet muodostavat ryhmiä, joiden sisällä piirteet ovat voimakkaasti kollineaarisia. Tämä olettamus mahdollistaa piilomuuttajamalliin perustuvan dimensionaalisuuden pudotuksen, jonka ansiosta menetelmä on toimiva myös pienen näytemäärän havaintoaineistoille. Menetelmä käsittelee havaintoaineistoa täysin bayesilaisittain, Gibbsin otannan avulla. Bayesilainen lähestymistapa tuottaa arvion sekä mallin ja havaintoaineiston yhteisjakaumalle että mallin jokaisen parametrin marginaalijakaumalle. Tämä mahdollistaa tulosten epävarmuuden arvioinnin sekä vertailun toisiin malleihin. Uuden menetelmän toimivuutta esitellään metabolomiikan alalta olevan havaintoaineiston avulla. Aineisto sisältää lipidiprofiileja, jotka on mitattu terveistä lapsista ja lapsista, jotka myöhemmin sairastuvat tyypin 1 diabetekseen. Kahdessa erillisessä analyysissä tutkitaan sairauden ja sukupuolen sekä sairauden ja iän vaikutusta lipidiprofiileihin.Two-way experimental designs are common in bioinformatics. In this thesis, a new Bayesian model is proposed for the analysis of two-way data. The method also works for small sample-size data with a high number of features. The data set is assumed to be divided into populations according to covariates, which in the case of a typical biological experiment are the health status, the gender, the medical treatment and the age of the individual. The proposed method is designed to estimate the effect of these covariates compared to the ground level of a control group of the data. The method is based on the assumption that features of the data form groups that are highly collinear. This allows the use of a latent variable-based dimensionality reduction, which makes inference possible also for small sample-size data sets. The method treats the data in a completely Bayesian way, which produces an estimate for the joint distribution of the model and the data, and marginal posterior distributions of all model parameters. This allows one to evaluate the signicance and uncertainty of the results and to compare it to other models. Inference is carried out with Gibbs sampling. The performance of the new method is demonstrated with a metabolomic data set by comparing lipidomic profiles from children who remain healthy to those who will later develop type 1 diabetes. In two separate studies, the effect of the disease and gender, and the effect of the disease and time, are estimated

Transverse Momentum Broadening and the Jet Quenching Parameter, Redux

We use Soft Collinear Effective Theory (SCET) to analyze the transverse momentum broadening, or diffusion in transverse momentum space, of an energetic parton propagating through quark-gluon plasma. Since we neglect the radiation of gluons from the energetic parton, we can only discuss momentum broadening, not parton energy loss. The interaction responsible for momentum broadening in the absence of radiation is that between the energetic (collinear) parton and the Glauber modes of the gluon fields in the medium. We derive the effective Lagrangian for this interaction, and we show that the probability for picking up transverse momentum k_\perp is given by the Fourier transform of the expectation value of two transversely separated light-like path-ordered Wilson lines. This yields a field theoretical definition of the jet quenching parameter \hat q, and shows that this can be interpreted as a diffusion constant. We close by revisiting the calculation of \hat q for the strongly coupled plasma of N=4 SYM theory, showing that previous calculations need some modifications that make them more straightforward and do not change the result.Comment: 18 pages, 7 figures; v2, minor revisions, references added; v3, version to appear in Phys. Rev. D: Feynman rules corrected, improved explanations of the gauge invariance of our calculation and of how the scaling of SCET operators differs from that in other contexts in the literature; no changes to any result

When Effective Field Theories Fail

In this talk, I describe and defend four non-standard claims about four effective field theories, and try to extract some lessons about the limits of effective field theory. The four theses (and a capsule diagnosis given in parentheses) are: 1) Kaon loops are not a reliable part of chiral perturbation theory (dimensional regularization does not know about the chiral scale), 2) Regge physics is inappropriately missing from SCET (an infinite set of scales are needed) 3) There is likely a barrier in the use of EFT in general relativity in the extreme infrared (curvature effects build up) and 4) Gauge non-invariant operators should be included in describing physics beyond the Standard Model (as they could probe the idea of emergent gauge symmetry and falsify string theory).Comment: Opening talk at the International Workshop on Effective Field Theories, Valencia, 2-6 February 2009. 15 pages, 6 figure